Question

a) The capacity of a memory chip is specified as 64K x 8 bits. Find out the address lines & the data lines for the chip. b) A memory block has 20 address lines & 16 data lines. Specify its capacity c) Assume a 32-bit microprocessor is to be used in a computer system, what is the size of its address bus, data bus, control bus and the registers if it needs to access up to 32GB of data? Assume that each memory locations can store a 32-bit word.

Answer 1

a) Assuming that number of address lines (address bits) is n, how can we find n? If n=1, you can only address 2 locations (0 and 1). If n=2, you can address 4 locations (0, 1, 2, and 3). As you can see, number of addressable locations = 2^n.
Given that number of addressable locations = 1024, then 1024=2^n
This means that Address line n=l log(64*1024) to the base 2=16
Thus, n=16.

You have 8 bits for every location, therefore your memory needs a data bus with 8 lines. Every time you read a location (by loading its address on the address bus), the 8 bits that are stored at that location are loaded (by the memory chip) on the 8-line data bus.

b)  A memory block has 20 address lines & 16 data lines. Its capacity is=1024KX16

c)

In computer architecture, 32-bit integers, memory addresses, or other data units are those that are 32 bits (4 octets or 4 Bytes) wide. Also, 32-bit CPU and ALU architectures are those that are based on registers, address buses, or data buses of that size. 32-bit microcomputers are computers in which 32-bit microprocessors are the norm. We know that n-bit microprocessor can handle n-bit word size.

As n-bit register can store 2ⁿ different values so, a 32-bit register can store 2³² different values. The range of integer values that can be stored in 32 bits depends on the integer representation used. We know there are two most common representations for integer data. And they are Unsigned and Signed representations. The range is 0 through 4,294,967,295 (2³² − 1) for representation as an Unsigned binary number, and −2,147,483,648 (−2³¹) through 2,147,483,647 (2³¹ − 1) for representation as two's complement Signed numbers.

One important consequence is that a processor with 32-bit memory addresses can directly access at most 4 GB of byte-addressable memory. But due to some issues, though in practice the limit may be lower.